Find the type of quadrilateral with the given ratio 2:3:4:1

Question

Find the angles of quadrilatatral whose ratio is 2:3:4:1. Ditermine the type of quadrilatatral?

Answer 1

The angles of a quadrilateral sum to 360°. If the angles are in the given ratio, and the smallest angle is x then x+2x+3x+4x=360, so 10x=360, x=36°, and the angles are 36°, 72°, 108°, 144°.

If the angles 36° and 144° are opposite one another then angles 72° and 108° will also be opposites. The sum of these opposites is 180°, so the quadrilateral would be cyclic (sits in a circumscribed circle with all its vertices on the circumference).